a car travels half distance with the speed of 20m/s and next half distance travel with 30 m/s , the average speed of the car is

The car travels half the distance by 20 m/s and the other half of the distance by 30 m/s .

Let the total distance be 2 x such that the half distance is x .

Let the total time taken be T .

Let the time taken for the first distance be t1 and the second distance be t2 .

So we can write that T = t1 + t2 because the total time taken is the sum of the time taken for the first half and the time taken for the second half .

Let the average speed be S .

Speed = distance / time

⇒ time = distance / speed

For the first distance

t1 = x / ( 20 )

⇒ t1 = x / 20

For the second distance

t2 = x / ( 30 )

⇒ t2 = x / 30

For the whole distance

T = 2 x / S

Adding t1 + t2 gives T

T = t1 + t2

⇒ T = x / 20 + x / 30

⇒ 2 x / S = x ( 1/20 + 1/30 )

⇒ 2 / S = ( 1/20 + 1/30 )

⇒ 2 / S = ( 3 + 2 ) / 60

⇒ 2 / S = 5 / 60

⇒ 2 / S = 1 / 12

⇒ S = 12 × 2

⇒ S = 24